The variable x is called the independent variable of function f and variable y is called the dependent variable of function f. We clear the concept of dependent and independent variable of function by figure

REAL VALUED FUNCTION:

For now onward, we shall only consider the function in which the variables are real numbers, and we say that f is a real value function of real number

Real valued function example

EXAMPLE:

We have the function f(x) = x³-2x²+4x-1

(i) f(0) = ?

f (x) = x³-2x²+4x-1

f(0)=0-0+0-1= -1

(ii) f(1) =?

f (x) = x³-2x²+4x-1

f(1) = 1-2+4-1 = +2

(iii) f(-2) = ?

f (x) = x³-2x²+4x-1

f(-2)= (-2)³-2(-2)²+4(-2)-1

= – 8- 8-8-1= -25

(iv) f(1+x) =?

f (x) = x³-2x²+4x-1

f(1+x)= (1+x)³-2(1+x)²+4(1+x)-1

f(1+x) = x³+x²+3x+2

(v) f(1/x) =? Where x ≠ 0

f (x) = x³-2x²+4x-1

f(1/x)=(1/x)³-2(1/x)²+4(1/x)-1

= 1/x³-2/x²+4/x-1 Where x ≠ 0

Function notation:

if a variable y depends on a variable x in such a way that

each value of x determine exactly one value of y, then we say that

“y is a function of x”

Swiss mathematician Euler(1707-1783) invented a symbolic way to

write the statement “y is a function of x”

as y=f(x) which read as” y is equal to x”

Explanation of function:

A function can be considered as a computing machine f that takes an input x,

exactly one output f(x). This output f(x) is called the value of f at x or image of x under f.

The output f(x) is denoted by a single letter, say y, we write y= f(x)

Definition of function, domain, range

A function f from a set X to a set Y is a rule or a correspondence that assigns

to each element x in X a unique element y in Y. the set X is called the Domain of f.

The set of corresponding element y in Y is called the Range of f.